5.5 Theory of Pulsar Timing System
339
residuals. However, by using the Sigma-z variance, it is difficult to discriminate the
“blue” noise process with α ≥ 3.
5.5.4 Stability of Comparing PT with ATI
The pulsar timing observation is based on Atomic Time (AT). Using the pulse TOA
measurement data for many years, the parameters related to pulsars, such as the
pulse phases, frequencies and their rates, as well as the angular positions, proper
motions and parallaxes of the pulsars, can be accurately estimated, and then the
timing residuals are the difference between the reference AT and Pulsar Time (PT),
namely, AT–PT. In order to ensure the accuracy of the PT, the TAI or TT is usually
taken as the reference to calculate the PT. The millisecond pulsars have the extremely
stable rotation frequencies and their signals can be read out cumulatively. Therefore,
the PT can be compared with other timescales, and it has the performance of ordinary
clocks.
Since 1982, two millisecond pulsars PSR B1937+21 and PSR B1855+09 have
been observed at the Arecibo Observatory for the long term, accumulating 16 years
of observational data. Using the observation data with a time span of 3300 days and
adopting the Sigma-z variance statistical analysis method, the residuals of the PT
from B1937+21 and B1855+09 relative to the Terrestrial Time in 1996 (TT96) was
calculated by Demetrios N. Matsakis, et al. In addition, the statistical results of the
Sigma-z timing residuals on several terrestrial timescales are also presented. From
the studied results, it can be shown that:
(1) The slopes of Sigma-z variance curves of the two pulsars are −1.5 or so during
the sampling interval of 3 years, and the timing residuals are mainly caused
by independent measurement errors. When the sampling interval is more than
1 year, the timing residuals are mainly caused the low-frequency noises, which
are generally considered as the inherent noise between the pulsar’s and atomic
timescales.
(2) With the sampling interval increasing, the frequency stability curve of PSR
B1855+09 always demonstrates a downward trend, while the stability of PSR
B1937+21 is greatly affected by the higher order derivatives of the rotational
period, and thus it gradually shows upward trend during the final segment.
(3) When the sampling interval is more than 1 year, by comparing the time residuals
of TT96–PT(1937) with those of TT96–PT(1855) and TA(PTB)–TA(A.1), and
considering the equivalence of TT96 and TA(PTB), the frequency stability
of the PT has reached or been better than that of TA(A.1). Among them,
PT(1937) and PT(1855) denote the pulsar times from PSR B1937+21 and
PSR B1855+09, respectively; TA(A.1) denotes the atomic time maintained by
the U.S. Naval Observatory; TA(PTB) denotes the atomic time maintained by
the Federal Physical Institute of Germany.
339
residuals. However, by using the Sigma-z variance, it is difficult to discriminate the
“blue” noise process with α ≥ 3.
5.5.4 Stability of Comparing PT with ATI
The pulsar timing observation is based on Atomic Time (AT). Using the pulse TOA
measurement data for many years, the parameters related to pulsars, such as the
pulse phases, frequencies and their rates, as well as the angular positions, proper
motions and parallaxes of the pulsars, can be accurately estimated, and then the
timing residuals are the difference between the reference AT and Pulsar Time (PT),
namely, AT–PT. In order to ensure the accuracy of the PT, the TAI or TT is usually
taken as the reference to calculate the PT. The millisecond pulsars have the extremely
stable rotation frequencies and their signals can be read out cumulatively. Therefore,
the PT can be compared with other timescales, and it has the performance of ordinary
clocks.
Since 1982, two millisecond pulsars PSR B1937+21 and PSR B1855+09 have
been observed at the Arecibo Observatory for the long term, accumulating 16 years
of observational data. Using the observation data with a time span of 3300 days and
adopting the Sigma-z variance statistical analysis method, the residuals of the PT
from B1937+21 and B1855+09 relative to the Terrestrial Time in 1996 (TT96) was
calculated by Demetrios N. Matsakis, et al. In addition, the statistical results of the
Sigma-z timing residuals on several terrestrial timescales are also presented. From
the studied results, it can be shown that:
(1) The slopes of Sigma-z variance curves of the two pulsars are −1.5 or so during
the sampling interval of 3 years, and the timing residuals are mainly caused
by independent measurement errors. When the sampling interval is more than
1 year, the timing residuals are mainly caused the low-frequency noises, which
are generally considered as the inherent noise between the pulsar’s and atomic
timescales.
(2) With the sampling interval increasing, the frequency stability curve of PSR
B1855+09 always demonstrates a downward trend, while the stability of PSR
B1937+21 is greatly affected by the higher order derivatives of the rotational
period, and thus it gradually shows upward trend during the final segment.
(3) When the sampling interval is more than 1 year, by comparing the time residuals
of TT96–PT(1937) with those of TT96–PT(1855) and TA(PTB)–TA(A.1), and
considering the equivalence of TT96 and TA(PTB), the frequency stability
of the PT has reached or been better than that of TA(A.1). Among them,
PT(1937) and PT(1855) denote the pulsar times from PSR B1937+21 and
PSR B1855+09, respectively; TA(A.1) denotes the atomic time maintained by
the U.S. Naval Observatory; TA(PTB) denotes the atomic time maintained by
the Federal Physical Institute of Germany.